Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function

Liu, Lie and Mao, Xuerong and Cao, Jinde (2019) Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function. Journal of Mathematical Analysis and Applications, 479 (2). pp. 1986-2006. ISSN 0022-247X

[img] Text (Liu-etal-JMAA-2019-Razumikhin-type-theorem-for-stochastic-functional-differential-systems)
Liu_etal_JMAA_2019_Razumikhin_type_theorem_for_stochastic_functional_differential_systems.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 16 July 2020.
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (228kB) | Request a copy from the Strathclyde author

    Abstract

    This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.